I'm looking for an example of a graph whose automorphism group is the alternating group on 4 symbols, A_4. If there is a construction that generalizes to an arbitrary alternating group, then I would love to know it.
2026-03-30 16:43:29.1774889009
A graph whose automorphism group is the alternating group
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$A_4$ is the group of symmetries of a regular tetrahedron that preserve orientation. So something like this should work:
This construction can be generalized recursively to larger alternating groups -- for example, for $A_5$ take the complete graph $K_5$ and replace each of the vertices with a copy of the above graph, suitably oriented.